1. Field of the Invention
The invention relates to active filters and comprises an active band-reject filter of the state-variable type.
2. Prior Art
Active filters are electrical filters containing one or more active elements such as amplifiers. The active elements enable one to obtain the desirable characteristics of RLC filters without using any inductors. The resultant filters are generally smaller, cheaper, and readily adapted to integrated circuit realization. State-variable filters are filters which are designed in accordance with a particular synthesis technique ("state variable synthesis"). These filters are characterized by the use of active integrators and summers connected in a closed loop.
A band-reject filter ideally has zero transmission over a selected band (the "rejection band") and a finite transmission elsewhere. In state-variable filters, the band reject function is typically synthesized by summing the outputs of a low-pass filter and a high-pass filter or by summing the input signal with the output of a band-pass filter. In the former method, peaking effects require one to limit the gain within the filter to avoid overloading or saturating the active elements; this necessitates an increase in the gain of the summing elements which causes an increase in the output noise. This is especially a problem when the filter Q is high. In the latter method, only a limited number of filter circuits are available which provide the necessary unity gain in the band-pass filter output at the band-reject center frequency. Of these, the circuit most suited to broadband tuning requires the use of non-inverting, as well as the inverting, inputs of one or more of the active amplifier elements in the filter. The use of the non-inverting input restricts the use of compensation techniques which can improve the gain-bandwidth response, and thus the performance of the circuit is limited by the non-inverting amplifier. To improve circuit response, therefore, one must utilize a high quality amplifier, and this is quite expensive.
A further limitation on filter circuits is imposed by the non-ideal nature of filter circuit elements, such as finite amplifier loop gain at d.c. frequency, frequency dependent amplifier amplitude variations and phase shift characteristics, and the existence of resistance in capacitors. These factors can seriously degrade circuit performance.